To determine the minimum amount Rafael should charge per cup of punch to make a $10 profit, we first need to calculate the total cost of the ingredients.
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Calculate the cost of raspberry sorbet:
- A gallon is equal to 4 quarts.
- The cost of a quart of sorbet is $4.00.
- Therefore, the total cost for a gallon of sorbet is: \[ 4 , \text{quarts} \times 4 , \text{dollars/quart} = 16 , \text{dollars} \]
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Calculate the cost of lemon-lime soda:
- Rafael needs 2 liters of lemon-lime soda.
- The cost of a 2-liter container is $3.00.
- Thus, the total cost for the soda is: \[ 3 , \text{dollars} \]
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Calculate the total cost of the punch ingredients:
- Total cost = Cost of sorbet + Cost of soda \[ 16 , \text{dollars (sorbet)} + 3 , \text{dollars (soda)} = 19 , \text{dollars} \]
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Add the desired profit:
- Rafael wants to make a $10 profit.
- Total profit needed = Total cost + Desired profit \[ 19 , \text{dollars (total cost)} + 10 , \text{dollars (profit)} = 29 , \text{dollars} \]
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Calculate the price per cup:
- Rafael makes 12 cups of punch.
- The minimum amount he should charge per cup is: \[ \frac{29 , \text{dollars}}{12 , \text{cups}} \approx 2.4167 , \text{dollars/cup} \]
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Round to the nearest hundredth:
- When rounded to the nearest hundredth, the price per cup is: \[ 2.42 , \text{dollars} \]
Thus, the minimum amount Rafael should charge per cup of punch in order to make a $10 profit is $2.42.